Cool ways to calc pi





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Discus: College Confidential Café: 2004 Archive: Cool ways to calc pi
By Haithman (Haithman) on Sunday, June 27, 2004 - 01:36 am: Edit

We basically hijacked Daromanian's thread with calculating pi, so if you know of a cool way to calculate pi post here...

By Tongos (Tongos) on Wednesday, June 30, 2004 - 08:06 pm: Edit

I've got a really cool way to calculate pi haithman, have you taken calculus? (5 on test) This is the general formula. (Tan(180/infinity)) and multiply this by infinity. you can sub infinity with a really huge number. This is a method where you would insribe polygons with several sides inside a circle. Now, show me a way of how to calculate the volume of a sphere by using polyhedra (im kidding). or a four dimensional sphere, na i'm getting ahead of myself.

By Haithman (Haithman) on Wednesday, June 30, 2004 - 08:54 pm: Edit

Well I believe for your question of calculating volume using polyhedra you would have to use Gaussian Integrals? and im not that good yet. Maybe I can try it out later.
Nope, Ive yet to talk Calc, but i like to self study it when i get bored.

By Tongos (Tongos) on Wednesday, June 30, 2004 - 08:56 pm: Edit

that's exactly what I do, Haithman, i study calculus and number theory in my spare time not only when i get bored. I'm familiar with such vectors and gaussian curves. Right now, I'm trying to find a way to find zeros of complex polynomials, any input

By Haithman (Haithman) on Wednesday, June 30, 2004 - 09:01 pm: Edit

Here's what I posted in an earlier post on how to calculate the value of pi...

If you're for real, you would calculate pi by finding the area of a portion of a semicircle, and the area of a triangle in the semi-circle, add these two bad boys together, find the measure of the arc that this space encompasses. that measure over 360 multiplied by the formular for the area of a circle. Then when you solve for pi, denominator of the area of the sector, multiplied by the area of the triangle plus the area of the curve gives you pi.
Of course, you need to use integral calc and the bino theorem in the process, but thats basically how you's do it.

By Haithman (Haithman) on Wednesday, June 30, 2004 - 09:07 pm: Edit

Thats awesome man! Yeah I love math..
I dont know if I cant comment on finding zero's of complex polynomials.
Hmm Ill have to do some work I guess

By Tongos (Tongos) on Wednesday, June 30, 2004 - 09:40 pm: Edit

Yes, yes ofcourse, come to this place, i would love to talk math with you, Haithman. Good job!
Its wierd, because people think I'm wierd for studying math on my free time. I'm a bit akward, i guess. But there is something about math that really gets to me. That moment of ah! in finding the answer. This is my main interest. I hate textbooks though, how can one take advantage of memorizing formulas and completely neglecting the basis of the formula. I try to go through math by the proof approach, I find fun in my own ideas.

By Haithman (Haithman) on Wednesday, June 30, 2004 - 10:00 pm: Edit

Excellent! Well it looks like you have come to the right place. Many people on these boards are excellent at mathematics, and many do it on their free time. There is nothing to be ashamed about, that is how people make great strides in the world of mathematics.
Excellent!

By Twinkletoes696 (Twinkletoes696) on Wednesday, June 30, 2004 - 11:16 pm: Edit

Isn't it 22/7?

Or am I horribly mistaken? (*dodging evil looks from those who understand math*)

By Tongos (Tongos) on Wednesday, June 30, 2004 - 11:16 pm: Edit

Sorry, I couldnt get back to you in time. Yeah, I'm new to this site actually. I don't really worry all about tests like a lot of people do on this site. When the SAT, comes it comes, and thats my score. i dont really make a big deal out of tests. have you ever visited dr. math. and also, i would love to see some of your math work.

By Tongos (Tongos) on Wednesday, June 30, 2004 - 11:20 pm: Edit

no its not 22/7 because any number divided by a one digit integer will be known as a rational repeating number. this is only an approximation, and pi, by the way is irrational. otherwise, why would people go through so much trouble to find a pattern in pi

By Twinkletoes696 (Twinkletoes696) on Wednesday, June 30, 2004 - 11:24 pm: Edit

"otherwise, why would people go through so much trouble to find a pattern in pi"

I honestly don't know. Someone told me it was 22/7 and I just went with that for a long time. I used to always just calculate pi as 3.14... then my math teacher explained to me why I had to hit the pi button on my calculator instead of 3.14 because apparently it makes a big difference in your answer when calculating problems.

Does anyone know the highest number of digits that have been figured out after the decimal point?

By Tongos (Tongos) on Wednesday, June 30, 2004 - 11:26 pm: Edit

Something like a billion or something, i really am not sure. i dont really see a point in finding the digits of pi, its dumb.

By Tongos (Tongos) on Wednesday, June 30, 2004 - 11:40 pm: Edit

Haithman, your really going to seek pleasure in calculus. as did i. Unfortunatly, i didnt do to well in my other classes, because I studied math during those classes. When i got home, i constantly for hours studied math. seeking pleasure in such game. at the dinner table, i would be like, solve a cubic or quartic. my family would be looking at me all wierd, okay????
By the way, I had trouble solving this:
X^X=5
does anybody have a solution?

By Jenesaispas (Jenesaispas) on Wednesday, June 30, 2004 - 11:46 pm: Edit

Yes. It's 2.12937248276...

Method: giving the TI-89 a big headache.:)

Sorry I couldn't be of real help.

By Tongos (Tongos) on Wednesday, June 30, 2004 - 11:49 pm: Edit

thanks, anyway, how did you do it? do you have a method?

By Tongos (Tongos) on Wednesday, June 30, 2004 - 11:55 pm: Edit

Now, using a graphing calculator, couldnt you just input the function X^X-5=y and y=0. and use calc on the calculator to find the intersection?

By Alejandro (Alejandro) on Thursday, July 01, 2004 - 12:36 am: Edit

my god is this how ur spending ur summer? calculating pi?

By Haithman (Haithman) on Thursday, July 01, 2004 - 12:56 am: Edit

Tongos ive noticed you like number theory and finding proofs. Are you familiar with Euler's Pentagonal Number theorem? If so, have you come up with a proof for it?

By Digmedia (Digmedia) on Thursday, July 01, 2004 - 06:55 am: Edit

My favorite way of calculating pi:

Take a large piece of thick paper and cut two pieces from it. The first is a square with a side of any length you want. The second is a circle scribed with a radius of the same length. Fold the papers up and carefully weigh them. The ratio of their weights is pi.

By Jenesaispas (Jenesaispas) on Thursday, July 01, 2004 - 09:55 am: Edit

Oh, Tongos, all I did was enter...

solve(x^x=5,x)=2.129...

By Tongos (Tongos) on Thursday, July 01, 2004 - 11:53 am: Edit

Its E(-1)^nq^(n(3n-1)/2=Pro(1-q^n)
Where the sum goes from -infinity to positive and infinite product goes from 1 to infinity.
n(3n-1)/2 is a pentagonal number which goes by the inductive sequence 1,5,12.....
I know it follows the jacobis triangle
and yes alejandro, this is basically all that im doing this summer, math isnt it great. well i might go backpacking in a couple of week

By Alejandro (Alejandro) on Thursday, July 01, 2004 - 05:55 pm: Edit

bagpacking sounds like fun...take this time to do sumthin different, uve got plenty of math classes to come to calculate pi

By Haithman (Haithman) on Thursday, July 01, 2004 - 06:45 pm: Edit

Yeah you're right.

By Tongos (Tongos) on Thursday, July 01, 2004 - 07:09 pm: Edit

I had to go somewhere for five hours or so, right now its four o clock. So i couldn't write in for that block of time, between 11 and 4. I'd love to talk more about math. Yes, backpacking does sound really fun right now, haithman and alejandro. There's nothing better than doing old calculus on the top of mt. shasta or on mt whitney! show me some more of your math, haithman. calculus.

By Tongos (Tongos) on Thursday, July 01, 2004 - 07:58 pm: Edit

another way to calculate pi is to use the well known series. i forgot what it actually was, but this rings a bell
squareroot of (1+1/(2^2)+1/(3^2)+1/(4^2).....)6 which i think follows the wallis integral? yes?
right now i'm working on a way to find out the selection of certain numbers out of the area under the curves to create inductive series. To really understand the basis of the integral, one must go through difficult measures to create an inductive sum series. Let's try to somehow do this in an opposite fashion. given the integral, can we find the sum of the nth terms in the function?

By Tongos (Tongos) on Thursday, July 01, 2004 - 09:38 pm: Edit

what tongos is saying is he needs to get out more!

By Zhalefarin (Zhalefarin) on Thursday, July 01, 2004 - 09:43 pm: Edit

X^X=5 has many solutions... c'mon people if x is even or odd has big implications as well as positive or negative. I have a ti-89 and can verify that it does say that x=2.12937 but it also says "caution: other solutions may exist"

tsk... tsk... tsk...

By Tongos (Tongos) on Thursday, July 01, 2004 - 09:48 pm: Edit

what, imaginary solutions can exist, yeah.....

By Tongos (Tongos) on Thursday, July 01, 2004 - 09:50 pm: Edit

Furthur more, if it can be multiplied by an integer and created into an even then it will have other solutions, but given that the power and the co is irrational.........

By Daromanian (Daromanian) on Thursday, July 01, 2004 - 10:36 pm: Edit

ln 5/ln x = x
x * ln x = ln 5
e^x = 5^(1/ln x)

and voila, nothing accomplished lol

By Tongos (Tongos) on Thursday, July 01, 2004 - 11:28 pm: Edit

this can't be done algebraically friends, please someone prove me wrong. although i did find a neat correlation between this and the taylor series. try integrating the function.

By Steveruleworld (Steveruleworld) on Monday, July 05, 2004 - 04:57 am: Edit

I am almost absolutely positive that pi can be found to any aproximation using Taylor series, I remember one of my teachers, a math genious, talk to us about how to find it, but i forgot what equation he used. I don't normally stress over math too much, but i'll try to find the equation that we used to aproximate it.

By Psa (Psa) on Monday, July 05, 2004 - 12:17 pm: Edit

I just love this fraction 355/113...

See!? 113355!

By Tongos (Tongos) on Monday, July 05, 2004 - 01:17 pm: Edit

yes, the beautiful world of mathematics, several ways to get to the solution! still, has anybody WITHOUT a graphing calculator WITHOUT the worry about multiple solutions solve x^x=5

By Mahras (Mahras) on Monday, July 05, 2004 - 03:11 pm: Edit

I am not that uber hot is math. I am good but not as good as doing calc and number theory as a soph. Oh well.....I like reading history and researching the market for fun.

By Mahras (Mahras) on Monday, July 05, 2004 - 03:22 pm: Edit

And guys are there any websites which have tutorials in math?

Thanks

By Tongos (Tongos) on Monday, July 05, 2004 - 05:40 pm: Edit

dr. math, these guys are genius, submit any questions you have from 1+1 to x^x, they'll have full on solutions, helping you understand math rather than just giving you the answer.

By Fenix_Three (Fenix_Three) on Monday, July 05, 2004 - 06:28 pm: Edit

I can't understand math in written form.

By Haithman (Haithman) on Monday, July 05, 2004 - 11:54 pm: Edit

Couldnt you calculate pi using the taylor series exp. for the inverse of tangent x? Although I think this is the one that converges excrutiatingly slowly, aka if you want to calculate pi to lets say 7 digits, you might need to sum up 10+ million terms (a guess)?
But what if you combine Machin's formula with a taylor series? Am I wrong to assume this is what they use today to calculate pi?
Hmm im probably talking nonsense, can someone please clarify?

Thank You

By Haithman (Haithman) on Tuesday, July 06, 2004 - 04:45 pm: Edit

bump

By Crazylicious (Crazylicious) on Tuesday, July 06, 2004 - 05:18 pm: Edit

you guys are nerds :)

By Haithman (Haithman) on Tuesday, July 06, 2004 - 06:04 pm: Edit

Have any insight crazylicious?

By Tongos (Tongos) on Tuesday, July 06, 2004 - 10:36 pm: Edit

haithman, i'll try it tonight, if i have time, and i will get back to you either late tonight of the day after tommorrow because i'm going to be hiking tommorrow. but i think i will give a response to your question. there's other math than needs working also

By Thermodude (Thermodude) on Friday, July 09, 2004 - 05:42 pm: Edit

Haithman...your idea of using the inverse arc-tangent for Pi is actually what most mathematicians had been using for the past 300 years up to 1950...if i'm correct. Remember 4 * (1 - 1/3 + 1/5 - 1/7 + 1/9....+ (-1)^(K + 1)/(2k - 1)).....well..that famous series for Pi is what you would get if you substituted in 1 for a taylor series of arc-tang....then you would just multiply the result by 4...since arc-tang of 1 is pi/4. Anyways...that would converge really slowly...but mathematicians such as Euler found ways to speed up that convergence by combining it with other series and stuff.

By Haithman (Haithman) on Friday, July 09, 2004 - 06:05 pm: Edit

Yeah Im old skool...
lol

By Jshifton (Jshifton) on Sunday, July 11, 2004 - 09:20 pm: Edit

I have an idea.

Pi is equal to circumfrence divided by diameter, so use a dL integral to calculate the circumfrence of a circle with x diameter, then divide by x.

For example, use the basic circle equation x^2 + y^2 = Radius^2. Then solve for Y, to get a Y=equation you can integrate.

So say the radius of our particular circle is 4, so we get Y=Sqrt(16-x^2). Then take the derivative of our particular equation to find Dy and Dx. Use Dl=Sqrt(Dx^2 + Dy^2), and integrate. Now we have half the length of our circle, because the original equation does not take into account the negative square root, so we double the value, and divide by 8 the diameter. This gives us Pi.

Any other ideas?

By Thermodude (Thermodude) on Monday, July 12, 2004 - 03:39 pm: Edit

This method, funny enough... looks VERY similar to finding a quarter of area of the circle y^2 + x^2 = 0. Notice that finding the circumference of a circle (Radius 1) would lead to the integral Sqrt(4x^2 + 1)...from 0 to 1. Finding the area would lead to the integral of Sqrt(1 - x^2)..from 0 to 1.


I'm sure both equations would be integrated in a similar manner....but you can't integrate it by using integration by parts. Doing so would end up with gettting a lot of division by zero and stuff. There must be some other way of integrating it...that I must have either carelessly overlooked...or just don't know of.

By Haithman (Haithman) on Monday, July 12, 2004 - 04:31 pm: Edit

Anyone have anymore problems?


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